Classifying finite-sheeted covering mappings of paracompact spaces.

Strongly base-paracompact spaces

A space X is said to be strongly base-paracompact if there is a basis B for X with |B| = w(X) such that every open cover of X has a star-finite open refinement by members of B. Strongly paracompact spaces which are strongly base-paracompact are studied. Strongly base-paracompact spaces are shown have a family of functions F with cardinality equal to the weight such that every open cover has a l...

Separation in Countably Paracompact Spaces

We study the question "Are discrete families of points separated in countably paracompact spaces?" in the class of first countable spaces and the class of separable spaces. Two of the main directions of research in general topology in the last thirty years have been the work of Jones, Bing, Tall, Fleissner, Nyikos and others motivated by the normal Moore space problem (when are discrete familie...

A Note on Paracompact Spaces

Let us quickly recall the definitions of the terms which are used in the statement of Theorem 1, and which will be used throughout this paper. Let X be a topological space. A collection <R of subsets of X is called open (resp. closed) if every element of "R. is open (resp. closed) in X. A covering of X is a collection of subsets of X whose union is X; observe that in this paper a covering need ...

Finite covering spaces of 3-manifolds

Following Perelman’s solution to the Geometrisation Conjecture, a ‘generic’ closed 3-manifold is known to admit a hyperbolic structure. However, our understanding of closed hyperbolic 3-manifolds is far from complete. In particular, the notorious Virtually Haken Conjecture remains unresolved. This proposes that every closed hyperbolic 3-manifold has a finite cover that contains a closed embedde...

Soft Connected Spaces and Soft Paracompact Spaces